Here's how this repair went. If you are relatively handy, and don't get scared by the sight of open electronics, it was pretty straight foward. Being super careful, it took me around 1-2 hours.
First thing you should do is watch Eric Gulbransen's video
on replacing the print head. It's not the same part, and its not even on the same side of the printer, but his walkthrough about how to take the outer shell of the printer off makes this process much much easier. Oh, then donate some buck to him to continue his excellent work.
Next, get copies of both Epson 7900 manuals: the "Epson 7900 Service Manual" and the "Epson 7900 Field Repair Guide". You can't buy them, and no one links to them. But if you do Google searches on them, you'll be able to find them. You will need both. They cover roughly the same info, but from different perspectives. I found that the Service Manual is better for disassembly, and the Field Repair Guide is better for re-assembly. Note that the Pump Cap Assembly is called the "Ink System" in the Service Manual (diagram on pg 55, replacement outlined on page 179), and is called the "Cleaning Unit" in the Field Repair Guide (detailed instructions for removal and installation on page 39).
Then, buy a new pump cap assembly. Epson part 1569512. I got mine from Compass Micro for around $231. Call Rod at 800-388-8595.
Follow the instructions to remove the Pump/Cap Assembly. I read through them like a dozen times first. It's a big part, but don't be intimidated - it's designed to be replaced, and is only held in by a few strategic screws.
When your 7900 is open, but BEFORE you remove the Assembly, be sure to LABEL each of the wires that connect the assembly to the sub-assembly circuit board. There are 18 of them, and if you just pull them out, you will have a heck of a time figuring out which goes where. First label the wires in the existing assembly. THEN label the wires in the new assembly. Double-check that you have them all.
When you pull the wires from the sub-assembly circuit board, they don't come out straight - you need to jog them slightly to the side to release.
That's really it - the manuals step you through the whole process. Hope this helps!